The movement of bodies in space (like spacecraft, satellites, and space stations) must be predicted and controlled with precision in order to ensure safety and efficacy. Kinematics is a field that develops descriptions and predictions of the motion of these bodies in 3D space. This course in Kinematics covers four major topic areas: an introduction to particle kinematics, a deep dive into rigid body kinematics in two parts (starting with classic descriptions of motion using the directional cosine matrix and Euler angles, and concluding with a review of modern descriptors like quaternions and Classical and Modified Rodrigues parameters). The course ends with a look at static attitude determination, using modern algorithms to predict and execute relative orientations of bodies in space.
After this course, you will be able to...
* Differentiate a vector as seen by another rotating frame and derive frame dependent velocity and acceleration vectors
* Apply the Transport Theorem to solve kinematic particle problems and translate between various sets of attitude descriptions
* Add and subtract relative attitude descriptions and integrate those descriptions numerically to predict orientations over time
* Derive the fundamental attitude coordinate properties of rigid bodies and determine attitude from a series of heading measurements

審閱

MB

This is a great course for beginners in kinematics, I enjoy it and learn so much. However, you need to have a good math background.

MA

Feb 08, 2018

Filled StarFilled StarFilled StarFilled StarFilled Star

Great professor. The material is very focused on space systems, but can easily be used in other robotics applications

從本節課中

Introduction to Kinematics

This module covers particle kinematics. A special emphasis is placed on a frame-independent vectorial notation. The position velocity and acceleration of particles are derived using rotating frames utilizing the transport theorem.

教學方

Hanspeter Schaub

Glenn L. Murphy Chair of Engineering, Professor

腳本

Hi, and welcome to this course sequence on spacecraft dynamics and control. My name is Hanspeter Schaub, and I'm a professor at the University of Colorado at Boulder. A little bit myself quickly. I do research on spacecraft dynamics, including formation flying, relative motion descriptions, and also some exciting work on chars astronomics. Where we're using electron guns and ion guns to create tractor beams essentially, to attract, repel spacecraft. I've also been involved on several spacecraft missions including as the ADCS lead on one of them. And I'm currently involved in a deep space mission doing attitude dynamics control applications. So this topic that you're about to hear about is very near and dear to my heart. What is this class going to cover? There are three main sections. After a brief introductory stuff about vectors and notations and so forth really to the three primary topics are going to be rigid body, kinematics, rigid body kinetics, and control. So what do these words actually mean? Kinematics is the description of motion. So that means if you go to rigid body which I've got my little foam cube here. Foam is always good when professors throws things around and when we drop him. So for what this means is, rigid body kinematics, we're describing the orientation, how do we now point space craft to point at a particular star and to look down and point at a Earth location and doing science I need to scan certain part of the atmosphere. How do we describe such motions and we've translation there is infinity of ways that you can describe your position relative to somebody else, there is distant and a heading that you can use like asthma elevation and direction but you can also use just regular cartesian coordinates go this far east, north, south, up down those kinds of coordinates, it attitude we have an infinity of ways to describe or in there's the classic yawning, pitching and rolling that people are familiar with, but there are a million other coordinates that have a lot of benefits. They all have challenges and they have benefits and we're going to go over both pros and cons of these and really show you fundamentally how to describe it. This is going to be now very, very useful because we can take and add it to the descriptions of object and you have attitude description of another object and then, you need to know the attitude of one relative to another. How do we add subtract orientation? What is fundamental operators? That's rigid body kinematics. The second section is rigid body kinetics. That means we are now taking into account mass inertia forces and torques acting on a spacecraft. So the thrusters out here firing and this whole thing starts to pitch and it starts to translate, how do you describe all these stuff mathematically? How do we derive these equations of motion to predict and how do we solve them numerically? And then we also look at system that are dual spinners. Sometimes, you have spacecraft that have a rigid part and another big rigid part that's spinning, that's a very popular communication satellite design some deep space missions, we'll look at gravity gradient torques, we're looking at a system of space craft equipped with multiple rotating wheels. Like control remote gyroscopes and reaction wheels and those devices. We also look at free spinning motion. In space, most of the time, we're not controlling because we don't have much fuel or energy. So, we have to exploit the natural dynamics and that will be a big chunk of kinetics as well. What's the naturally tumbling motions? How does this object like to move? Depending on it's shape, geometry mass distribution. Then the last chunk is Control. This is where we take the natural dynamics and go well this isn't quite stable. I want it to be pointing here in this direction and then we add feedback on top of it where you sense the environment you sense what’s going on and you say well I'm pointing about three degrees too low how do I change my wheel speed how do I twist. How do I apply torts, how do I apply thrusters to reorient this and guarantee that I will be stable, I won't overshoot it won't undershoot I can specify what the performance going to be and (UNKNOWN) attitude it's a non linear problem so we'll be dealing with non linear control definitions and we'll be looking at ways to actually define stability for very large departures not just small oscillators federation, so that kind of test this part apart. Everything else would be covered in this lectures. So that's the three main topic areas that we cover here and the course sequences you're about to see are actually coming from my lectures that I teach here every year at the University of Colorado. So we've taken out some of things that are very course specific like talking over homeworks and assignments and that different arrangements and we're getting to the guts of the technical stuff. That's what you'll be seeing, it's kind of edited together over the days. And we'll be adding supplementary material as well. But you're following along pretty much with the exact same material that we do in class. And I have posted a variety of problems that you can solve. That kind of parallels what we're learning in these These lectures. Another thing is textbook. These course sequences are set up and designed where I'm providing you everything here that you need to know from the lectures, from the slides and so forth. But if you want auxiliary reading, the class that I teach is really based on this textbook here called Analytical Mechanics of Space Systems. And it's a book that's used in many, many schools, I think over 20 schools now use it. Variety of aspects is based from dynamics and we do as well. So the material you're seeing is going to touch chapter one. Focus a lot on chapter three, that's the kinematics for kinetics. And then we jump to chapter eight, which deals with different nonlinear control solutions. So three, four and eight are the focus here and interest. But that's the quick intro. I really look forward to working you here, I hope you enjoy this material as much as I do. This is a class that I get a lot of feedback on from students who graduated, been in the industry for a while, worked at NASA, JPL, and then a few years later, see them again. They go, you know, Dr. That was a really useful stuff I handed that class, at the time maybe it was full of details but now that i'm using it this is material that I find that i'm using all the time, 3D representation dynamics is not just for space craft this is also sued for aircraft, surface vehicles, under water vehicles, robotics, even computer vision and gaming industry use some of this work how to describe orientation to computational efficiency and so forth. So, it's a great fundamental topic. We going to be applying it to space which is fine exciting application. But what you learn is the fundamentals of how to do rigid body dynamics. Thanks.